# Appendix 06: Critical Values for Dixon’s Q-Test

The following table provides critical values for Q(α, n), where α is the probability of incorrectly rejecting the suspected outlier and n is the number of samples in the data set. There are several versions of Dixon’s Q-Test, each of which calculates a value for Qij where i is the number of suspected outliers on one end of the data set and j is the number of suspected outliers on the opposite end of the data set. The values given here are for Q10, where

$Q_\ce{exp} = Q_{10} = \mathrm{\dfrac{|\textrm{outlier's value} - nearest\: value|}{largest\: value - smallest\: value}}$

The suspected outlier is rejected if Qexp is greater than Q(α, n). For additional information consult Rorabacher, D. B. “Statistical Treatment for Rejection of Deviant Values: Critical Values of Dixon’s ‘Q’ Parameter and Related Subrange Ratios at the 95% confidence Level,” Anal. Chem. 1991, 63, 139–146.

Critical Values for the Q-Test of a Single Outlier (Q10)
α⇒ 0.1 0.05 0.04 0.02 0.01
n
3 0.941 0.970 0.976 0.988 0.994
4 0.765 0.829 0.846 0.889 0.926
5 0.642 0.710 0.729 0.780 0.821
6 0.560 0.625 0.644 0.698 0.740
7 0.507 0.568 0.586 0.637 0.680
8 0.468 0.526 0.543 0.590 0.634
9 0.437 0.493 0.510 0.555 0.598
10 0.412 0.466 0.483 0.527 0.568